Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Xilu Wang; Xiaoliang Cheng

doi:10.3934/eect.2021064

Article Contents

2022, Volume 11, Issue 5: 1797-1811. Doi: 10.3934/eect.2021064

This issue Previous Article Stabilization of port-Hamiltonian systems with discontinuous energy densities Next Article Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Xilu Wang^, and
Xiaoliang Cheng

School of Mathematical Science, Zhejiang University, Hangzhou 310027, China

^*Corresponding author: Xilu Wang
^*Corresponding author: Xilu Wang

Received: June 2021

Revised: October 2021

Early access: January 2022

Published: October 2022

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Abstract

In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.

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Mathematics Subject Classification: Primary: 47J20, 47J22, 49J40.

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